Backport PR #57333 on branch 2.2.x (REGR: merge with 3rd party EA's can sometimes raise ValueError)

doc/source/whatsnew/v2.2.1.rst

@@ -22,6 +22,7 @@ Fixed regressions
 - Fixed regression in :meth:`.DataFrameGroupBy.idxmin`, :meth:`.DataFrameGroupBy.idxmax`, :meth:`.SeriesGroupBy.idxmin`, :meth:`.SeriesGroupBy.idxmax` where values containing the minimum or maximum value for the dtype could produce incorrect results (:issue:`57040`)
 - Fixed regression in :meth:`CategoricalIndex.difference` raising ``KeyError`` when other contains null values other than NaN (:issue:`57318`)
 - Fixed regression in :meth:`DataFrame.loc` raising ``IndexError`` for non-unique, masked dtype indexes where result has more than 10,000 rows (:issue:`57027`)
+- Fixed regression in :meth:`DataFrame.merge` raising ``ValueError`` for certain types of 3rd-party extension arrays (:issue:`57316`)
 - Fixed regression in :meth:`DataFrame.sort_index` not producing a stable sort for a index with duplicates (:issue:`57151`)
 - Fixed regression in :meth:`DataFrame.to_dict` with ``orient='list'`` and datetime or timedelta types returning integers (:issue:`54824`)
 - Fixed regression in :meth:`DataFrame.to_json` converting nullable integers to floats (:issue:`57224`)

pandas/_libs/index.pyx

@@ -295,7 +295,7 @@ cdef class IndexEngine:
                 values = self.values
                 self.monotonic_inc, self.monotonic_dec, is_strict_monotonic = \
                     self._call_monotonic(values)
-            except TypeError:
+            except (TypeError, ValueError):
                 self.monotonic_inc = 0
                 self.monotonic_dec = 0
                 is_strict_monotonic = 0

pandas/tests/indexes/test_base.py

@@ -1722,3 +1722,13 @@ def test_nan_comparison_same_object(op):
 
     result = op(idx, idx.copy())
     tm.assert_numpy_array_equal(result, expected)
+
+
+@td.skip_if_no("pyarrow")
+def test_is_monotonic_pyarrow_list_type():
+    # GH 57333
+    import pyarrow as pa
+
+    idx = Index([[1], [2, 3]], dtype=pd.ArrowDtype(pa.list_(pa.int64())))
+    assert not idx.is_monotonic_increasing
+    assert not idx.is_monotonic_decreasing